Dave Morris

A bijection f of a metric space is "distance-permuting" if the distance from f(x) to f(y) depends only on the distance from x to y. For example, it it is known that every distance-permuting bijection of the real line is the composition of an isometry...

Coxeter groups arise in a wide variety of areas, so every mathematician should know some basic facts about them, including their connection to "Dynkin diagrams." Proofs about these "groups generated by reflections" mainly use group theory, geometry...

In combinatorial geometry (and engineering), it is important to know that certain scaffold-like geometric structures are rigid. (They will not collapse, and, in fact, have enough bracing that they cannot be deformed at all.) Replacing the geometric...

Place a checker in some square of an m x n rectangular checkerboard, and glue opposite edges of the checkerboard to make a projective plane. We determine whether the checker can visit all the squares of the checkerboard (without repeating any squares...

The Traveling Salesman Problem asks for the shortest route through a collection of cities. This classical problem is very hard, but, by applying Linear Programming (and other techniques), the optimal route has been found in test cases that have tens...

For every generating set S of any finite group G, there is a corresponding Cayley graph Cay(G;S). It was conjectured in the early 1970's that Cay(G;S) always has a hamiltonian cycle, but there has been very little progress on this problem. Joint work...

We will discuss graphs that have a unique hamiltonian cycle and are vertex-transitive, which means there is an automorphism that takes any vertex to any other vertex. Cycles are the only examples with finitely many vertices, but the situation is more...